Symmetric Notches Research Articles

Construction of symmetrical and asymmetrical notches from elementary steps in isotropic plates

The interactions of the fundamental Lamb modes with discontinuities in an isotropic structure will be presented and analyzed in a simple and a fast way. The key point is to decompose the symmetrical or asymmetrical notch into two elementary steps. The fundamental antisymmetrical and symmetrical Lamb modes contributions are separated by means of the simple arithmetic operations of addition and subtraction. The power reflection and transmission coefficients are then computed with the well-known average power flow equation described in a previous work [NDT&E international, Vol. 41, p.1-9 (2008)]. Using these coefficients, the symmetrical notch can be constructed from one elementary symmetrical step while the asymmetrical notch is constructed from the superposition of asymmetrical down- and up-steps. Mode conversions phenomena are observed and analyzed for the asymmetrical steps and notches case. Finally, an experimental device is realized to test aluminum plates with different notch depths. Good agreement is found between experimental and numerical results.

Unique depinning fields at symmetric double notches in a ferromagnetic permalloy nanowire

Ferromagnetic domain-wall pinning and depinning mechanisms were investigated at permalloy nanowire notches using a micromagnetic calculation. A unique depinning field originated from the symmetric double notches irrespective of the wall polarity or the propagation direction, whereas several distinct pinning mechanisms appeared from single or asymmetric notches. The depinning field was principally determined by the exiting notch slope due to the dynamic narrowing of the domain wall thickness.

Micro-computed tomography of fatigue microdamage in cortical bone using a barium sulfate contrast agent

Accumulation of microdamage during fatigue can lead to increased fracture susceptibility in bone. Current techniques for imaging microdamage in bone are inherently destructive and two-dimensional. Therefore, the objective of this study was to image the accumulation of fatigue microdamage in cortical bone using micro-computed tomography (micro-CT) with a barium sulfate (BaSO 4) contrast agent. Two symmetric notches were machined on the tensile surface of bovine cortical bone beams in order to generate damage ahead of the stress concentrations during four-point bending fatigue. Specimens were loaded to a specified number of cycles or until one notch fractured, such that the other notch exhibited the accumulation of microdamage prior to fracture. Microdamage ahead of the notch was stained in vitro by precipitation of BaSO 4 and imaged using micro-CT. Reconstructed images showed a distinct region of bright voxels around the notch tip or along propagating cracks due to the presence of BaSO 4, which was verified by backscattered electron imaging and energy dispersive spectroscopy. The shape of the stained region ahead of the notch tip was consistent with principal strain contours calculated by finite element analysis. The relative volume of the stained region was correlated with the number of loading cycles by non-linear regression using a power law. This study demonstrates new methods for the non-destructive and three-dimensional detection of fatigue microdamage accumulation in cortical bone in vitro, which may be useful to gain further understanding into the role of microdamage in bone fragility.

Study of the fundamental Lamb modes interaction with symmetrical notches

The aim of this work is to predict the propagation of the fundamental Lamb modes in an isotropic structure containing discontinuities in a simple and a fast way. The key point is to decompose the symmetrical notch into two elementary abrupt changes in the plate section. The power reflection and transmission coefficients are computed, using two techniques, with the help of the finite element and the well-known average power flow equation. In the first technique, the through-thickness displacements and stresses are used while in the second technique only the normal or tangential displacement at a given location on the plate surface is used. An equality relation between the direct and the inverse abrupt changes of the plate section is given, which allows computing the power reflection and transmission coefficients for a symmetrical notch from those obtained from one elementary damage. Finally, aluminum plates with different notches depths are tested. Experimental and numerical results are in good agreement.

Fatigue Microdamage in Bovine Cortical Bone Imaged by Micro-Computed Tomography Using a Barium Sulfate Contrast Agent

AbstractAccumulation of microdamage during fatigue can lead to increased fracture susceptibility in bone. Current techniques for imaging microdamage in bone are inherently destructive and two-dimensional. A non-destructive, three-dimensional technique is needed to measure the spatial density of microdamage accumulation. Therefore, the objective of this study was to image microdamage accumulation in cortical bone during fatigue using micro-computed tomography (micro-CT) with a barium sulfate (BaSO4) contrast agent. Bovine cortical bone beams were loaded under four-point bending fatigue. Two symmetric notches were machined on the tensile surface in order to generate damage at the stress concentrations during loading. Specimens were loaded to a specified number of cycles or until one notch fractured, such that the other notch exhibited accumulated microdamage just prior to fracture. Microdamage ahead of the notch was stained by precipitation of BaSO4 and imaged using micro-CT. Reconstructed images showed a distinct region of bright voxels around the notch tip or along propagating cracks due to the presence of BaSO4, which was verified by backscattered electron imaging and energy dispersive spectroscopy. The stained region exhibited a characteristic kidney shape perpendicular to the notch tip, which was correlated to principal strain contours calculated by finite element analysis. The area of stained regions was positively correlated with the number of loading cycles.

Fracture strength of polysilicon at stress concentrations

Mechanical design of MEMS requires the ability to predict the strength of load-carrying components with stress concentrations. The majority of these microdevices are made of brittle materials such as polysilicon, which exhibit higher fracture strengths when smaller volumes or areas are involved. A review of the literature shows that the fracture strength of polysilicon increases as tensile specimens get smaller. Very limited results show that fracture strengths at stress concentrations are larger. This paper examines the capability of Weibull statistics to predict such localized strengths and proposes a methodology for design. Fracture loads were measured for three shapes of polysilicon tensile specimens - with uniform cross-section, with a central hole, and with symmetric double notches. All specimens were 3.5 /spl mu/m thick with gross widths of either 20 or 50 /spl mu/m. A total of 226 measurements were made to generate statistically significant information. Local stresses were computed at the stress concentrations, and the fracture strengths there were approximately 90% larger than would be predicted if there were no size effect (2600 MPa versus 1400 MPa). Predictions based on mean values are inadequate, but Weibull statistics are quite successful. One can predict the fracture strength of the four shapes with stress concentrations to within /spl plusmn/10% from the fracture strengths of the smooth uniaxial specimens. The specimens and test methods are described and the Weibull approach is reviewed and summarized. The CARES/Life probabilistic reliability program developed by NASA and a finite element analysis of the stress concentrations are required for complete analysis. Incorporating all this into a design methodology shows that one can take "baseline" material properties from uniaxial tensile tests and predict the overall strength of complicated components. This is commensurate with traditional mechanical design, but with the addition of Weibull statistics.

Two-axis flexure hinges with axially-collocated and symmetric notches

The paper introduces a new class of two-axis flexure hinges with axially-collocated and symmetric notches as an alternative to the existing flexure designs with serially-disposed notches. A generic formulation is developed in terms of the geometric curves defining the two notches which includes assessing the capacity of rotation, precision of rotation, sensitivity to parasitic effects, stress values, motion efficiency and shearing effects by means of compliance factors. Closed-form compliance equations are derived for a two-axis flexure hinge that is defined by two non-identical parabolic profiles. The analytical model predictions are confirmed by finite element data. A numerical comparison is made of the parabolic flexure with a constant rectangular cross-section flexure hinge in terms of several performance criteria.

Strength of a composite sheet material in impact tension

A procedure and results of studies on the strength of a 2-mm PA6 shock-resistant composite sheet in impact tension are briefly outlined. Experimental investigations include static and impact tensile tests of specimens with a short test portion and sharp symmetrical edge notches. Acoustic emission methods used in the tests of specimens in static tension revealed acoustic signals that point to the development of damages in the material under loads much lower than the ultimate one. Test procedures are similar to those used earlier for testing sheet metals in tension. The wave process in the specimens upon impact tension was analyzed using the viscoelastic model. The influence of viscosity on the width of the wave front, determining stress growth rates upon its propagation, was established. According to the test results, the change from quasistatic to impact tension slightly changes maximum stress levels. Impact tension of notched specimens in the first wave of loading lower than the ultimate one produces a decrease in stresses with time that can be determined by viscosity and damage effects near sharp notches.

Fracture Strength of Polysilicon thin Films at Stress Concentrations

AbstractThe fracture strengths of 3.5 microns thick and 20 or 50 microns wide polysilicon specimens were measured. One set of specimens was straight in the gage section, another set had a central hole 5.0 microns in diameter, and the third set had symmetric semicircular notches 2.5 microns in radius on each side. The local maximum fracture stresses of the non- uniform specimens, as calculated from the remote fracture stress with a stress concentration factor, were higher than measured in the straight specimens. This indicates a size effect, which is presumably due to the smaller highly stressed volume or area in the non-uniform specimens.

Fracture Performance of Progressively Drawn Pearlitic Steel under Triaxial Stress States

We study fracture processes in specimens with axially symmetric notches made of prestressed steels with various degrees of cold drawing of the wire. For this purpose, we use steel samples drawn to the required degrees. The intensity of drawing or the level of strains (characterized by the yield limit) is used as the main parameter of the technological treatment of the material. In specimens with notches of various shapes, we analyze the role of triaxiality of stresses. Special attention is given to the behavior of the sensitivity of the wire to notches as a function of triaxiality of stresses and the yield limit. The changes caused by the anisotropy of strength formed as a result of cold drawing are studied on the microscopic level.

Tensile Strength of Sheet Materials under Impact Loading

Test procedures are described and strength and plasticity results are presented for a 1.0-mm mild sheet steel and a 0.75-mm D16T high-strength aluminum alloy investigated under impact loading. The experimental investigations include tensile tests of sheet metal specimens with a short test portion and symmetric sharp edge notches. As is shown, the switch from static to impact loading over the range of tensile rates under study is accompanied by variations in the strength and plasticity of the tested metals. The region of residual strains near a sharp notch (determining the area of fracture initiation), formed as the result of tensile loads, is characterized by reduced maximum strains and a smaller length in the longitudinal direction. With distance from the boundary of the initial notch, the region of residual strains becomes extended.

Elastic stress distributions in finite size plates with edge notches

In fatigue crack growth analysis it is essential to know the stress distributions in the neighbourhood of stress raisers. If such distributions ahead of the uncracked notch are known, stress intensity factors may be obtained via the weight function or other methods. The procedure described in the present paper reconsiders the principal elastic stress expressions already reported by the authors for infinite plates with semi-infinite symmetric V-shaped notches and adapts them to some practical cases, in which the mutual influence of the notches as well as that of the plate finite size play an important role in stress distributions. The aim is therefore to give an approximate close-form solution for the longitudinal stress, valid for the entire ligament length, namely from notch tip to notch tip. Theoretical and numerical stress values are compared on this line, examining plates with semicircular, V and U-shaped notches subjected to remote uniaxial tension.

Fatigue crack initiation and propagation phases near notches in metals with low notch sensitivity

The paper summarizes the results of experimental work carried out in order to analyse the initiation and propagation of fatigue cracks on plates in a deep drawing steel and in a cast aluminium alloy. The plates were characterized by lateral V and U-shape symmetric notches, with a notch root radius ranging from 0.1 to 10 mm, the notch depth being 10 mm and the plate thickness 2 mm for the steel and 5 mm for the light alloy. In order to estimate the crack initiation life two new parameters are proposed; they are no longer based on the peak values of strain and stress, but on the averaged values of such quantities in the neighbourhood of the notch tip. The dimension of the process-zone is correlated to the intrinsic crack length of the material. The estimates need an elastoplastic approach and a numerical solution. Experimantal data and expected values are compared.

Stress analysis of anisotropic elastic V-notched bodies

A method to determine singular stress fields near a V-notch in an anisotropic plate is presented. The method is based on a new boundary element formulation recently proposed by Wu et al. [J. Appl. Mech.59, 344–348 (1992)] coupled with path-independent integrals relating the neartip field to the far field. Numerical examples are given for plates containing a single edge crack, two collinear edge cracks, an internal crack, a single notch, and two symmetric notches under uniform stress.

Crack curving under mode-I loading

The whole history of failure of a rectangular panel with two symmetrical notches and a central crack subjected to a progressively increasing tension load normal to the crack plane is studied. The material of the panel exhibits substantial plastic deformation prior to fracture. An elastic-plastic analysis of the plate is first performed based on finite elements. The results of stress analysis are coupled with the strain energy density theory to determine the critical load for crack initiation and the history of stable crack growth up to the point of instability. At instability the crack runs fast through the elastic material bypassing the plastic zone near the plate boundary. The crack deviates from its initial direction and is curved even though the plate is subjected to opening-mode loading. Results for crack trajectories are given for various initial crack lengths and notch radii of the plate.

Stress concentration of shoulder fillets in a flat bar under tension and in-plane bending. Effect of protuberances on the stress concentration.

This paper deals with the stress concentration analyses of fillets in an infinitely long strip with symmetric rectangular notches or protuberances under tensile load or in-plane bending moment. The stress field induced by a point force in a semi-infinite plate is used as a fundamental solution to solve those problems. The stress concentration factors are systematically calculated under various geometrical conditions. Through the comparison of the present results with the previous research works, it is found that the Peterson's stress concentration charts based on photoelastic tests gives underestimated stress concentration factors by about 10 %. The stress concentration factors of a stepped flat bar with fillets are found to be almost determined by the results of shoulder fillets in a semi-infinite plate.

Fracture instability of notched cracked plates characterized by the strain energy density theory

The fracture instability of a mechanical system is analyzed by the strain energy density theory. The local relative minima of the strain energy density function d W/d V referred to local coordinate systems at each point of the body are distinguished from the global minimum of d W/d V, G, which is referred to a fixed global coordinate system. Failure by fracture starts from the maximum of the local minima of d W/d V, L, and passes from point G. The distance l between L and G along the fracture trajectory is introduced as a length parameter to characterized the fracture instability of the system. Numerical results are obtained and discussed for a cracked plate with two symmetrical notches subjected to a monotonically rising tensile stress perpendicular to the crack axis.

切欠き深さおよび切欠き半径の異なる平面ひずみＵ形二重切欠き材の全面降伏強さに及ぼす干渉効果の上・下界法による検討

The overall yield strength of rectangular bar specimens with double symmetrical U-shaped notches of unequal depth and/or unequal radius was analysed by the upper and lower bound theorems. The occurance of interference between the two notches was thus studied. The yield strength for double notches became smaller because of the interference than that for a single notch. The amount of decrease in yield strength decreased with an increase of the difference in notch depth; so did the minimum distance between the notches at which the interference occurs. The interference did not occur below a certain distance. The difference in notch depth had stronger influence on the interference than the difference in notch radii. These analytical results can be easily applied to study the interference for double symmetrical notches of equal notch depth and equal notch radius, double symmetrical cracks and also for the combination of an extremely large notch radius and an extremely small notch radius.

切欠き深さおよび切欠き半径の異なるＵ形二重切欠き材の強度に及ぼす干渉効果の実験的検討

The interference effect of double symmetrical U-shaped notches of unequal notch depth and/or unequal notch radius on the strengths were investigated experimentally. The notch pitch range in which the general yield strength is reduced was able to be predicted by using the upper and lower bound theorems. The X-shape extension of plastic deformation occurred in the notch pitch range influenced by the interference effect. The notch tensile strength was also reduced by the interference effect. The magnitude of the reduction of notch strength ratio and the notch pitch range influenced by the interfarence effect were almost equal to thoes of the general yield stress ratio, or the ratio of the general yield stress at the net section of the notched bar to that of the smooth bar. The nominal mean stress at the net section at fracture was also reduced by the interference effect. The fracture along the inclined plane connecting two notches situated diagonally was caused by the X-shape extension of plastic deformation in the notch pitch range showing the strong interference effect. The fracture at the net section occurred in the notch potch range showing the weak interference effect. The difference in notch depth has much stronger influence on the interference effect than the difference in notch radius does.

Stress state of an annular plate with cyclically symmetrical curvilinear notches

Stress state of an annular plate with cyclically symmetrical curvilinear notches